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14 Wilson's Theorem



EBook Name14 Wilson's Theorem
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EBook Description: Wilson�s Theorem is elegant. It is not very useful, but like a lot of other people, I like it. So that is why it is here. Consider an integer n > 1. If the integer n-1! + 1 is divided by any number from 2 to n-1, it yields a remainder of 1.


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Electronic Transactions on Numerical Analysis

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16 Multinomials

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17 Stirling Numbers of the Second Type

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18 Matrices

Matrix algebra is also known as linear algebra and it is one of the most important disciplines of mathematics. It pervades virtually all of mathematics, but it could be argued to be closest to geometry. In this chapter, we will look at the relation between matrices and graphs.

19 Boolean Algebra

It has been known for sometime in mathematics that set algebras and Boolean1 algebras are different perspectives on the same thing. The treatment of sets here is informal and is known as naive set theory. Most of the time naive set theory is sufficient for the purposes of even professional mathematicians.

20 Probability and the Law of Addition

We are interested in the probabilities of events. Whatever events are, they are not numbers. Therefore, given events A and B, if I speak of the event A + B, it does not mean A plus B. Rather it is shorthand for A or B. Elsewhere,

21 PIE

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23 The Law of Multiplication

Probability trees are one of the most useful tools in probability and applied mathematics. We will use them throughout the rest of this text. The graph in Figure 1 is a probability tree.

24 The Bonferroni Inequality

1By far its most useful application is in joint confidence intervals. The inequality gives you a confidence interval without assuming independence of the various parameters. It usually turns out at around 95% confidence that the confidence region isn�t much smaller than with the assumption of independence.

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